I am supposed to factor the trinomial, y^2-xy-56x^2. How would I solve this from point A to point B?

Question

This is Algebra 2 work, and it is factoring trinomials. It is online schooling, so I can't ask my teacher. I chose one question from my work to enter into a step-by-step calculator on the internet to try to understand it. I figured if I could understand one question, then I could solve the rest on my own. I couldn't understand it, so could someone help with a good step-by-step explanation?

 

Again, I am supposed to factor the trinomial, y^2-xy-56x^2

Answer 1

Hi Jordan, to factor this start by setting up to sets of parenthesis like this:

 

(y     x) * (y    x)

 

Since there is a negative on the middle term and the third term, add the following to the set of parenthesis:

 

(y  -  x) * (y   +   x)

 

Now look at the coefficient for the x² term, what are the factors for 56:

 

1 and 56

2 and 28

4 and 14

7 and 8

 

Are there any others?

 

Which pair of factors when added or subtracted will give the coefficient of the middle, which is 1? 

 

Answer: 7 and 8.

 

Since the middle term is negative, the 8 goes with the minus sign and the 7 goes with the plus sign:

 

(y  -  8x) * (y  +  7x)

 

Questions?